The present invention relates to a sound field correcting system, and more particularly to a system for correcting the sound field at a predetermined listening point in the sound field receiving both sound waves radiated directly by a loudspeaker and reflected sound waves.
A typical example of an acoustic reproducing system is shown in FIG. 1. In FIG. 1, a reproducing signal outputted by a magnetic tape reproducing head 1-1 is amplified by a reproducing amplifier 1-2 and is then applied to a frequency characteristic adjusting amplifier 1-3. The output of the amplifier 1-3, after being subjected to power amplification by a loudspeaker drive amplifier 1-4, drives a loudspeaker 1-5.
In this system, the signal provided by the reproducing head 1-1 is converted into a signal having a desired frequency response characteristic and amplified by the reproducing amplifier 1-2. In the following stage, the frequency characteristic adjusting amplifier 1-3, for instance, a graphic equalizer or bass/treble control, converts the output signal of the amplifier 1-3 into a loudspeaker drive signal having a desired reproduction frequency characteristic.
In such an acoustic system, as shown in FIG. 2, a sound wave radiated by the loudspeaker 1-5 advances along two paths to reach a listening point (position) in the sound field. That is, at the listening point there are received both a direct sound wave (as indicated by the solid line 1-7) and a sound wave reflected from a wall or the like (as indicated by the dotted line 1-8). In this case, at the listening point 1-6, the two sound waves interfere with each other, as a result of which peaks and dips occur in the frequency characteristic so that the frequency response is made undesirable. In order to compensate for such an undesirable frequency response, the graphic equalizer 1-3 or the like is employed.
The reason why such peaks and dips occur in the frequency characteristic will be briefly described.
It is assumed that, in FIG. 2, the distance of the direct sound wave's path 1-7 to the listening point 1-6 is represented by L.sub.1, the distance of the reflected sound wave's path 1-8 to the listening point 1-6 is represented by L.sub.2, and the sound velocity is represented by c. Then, the sound S.sub.M at the listening point is the sum of the direct sound wave S.sub.S and the reflected sound wave S.sub.R : ##EQU1## where K is the reflection factor of a wall or the like and A is the signal strength at the surface of the loudspeaker. As for the reflected sound wave S.sub.R, it can be considered that the reflection is a so-called rigid edge in almost all cases, because the acoustic impedance of the wall is higher than that of air. It can be considered that the reflection takes place without change of phase. (In the case of a free edge reflection, the acoustic impedance is low, and S.sub.M =S.sub.S -S.sub.R.)
Expression (1) can be rewritten as follows: EQU S.sub.M =(A/L.sub.1)[e.sup.j.omega.(t-L.sbsp.1 .sup./c)+Be.sup.j.omega.(t-L.sbsp.2.sup./c)], (1-2)
where B=KL.sub.1 /L.sub.2.
If, for simplification of description, B is set to 1, the frequencies f where peaks occur are: EQU f=nc/(L.sub.2 -L.sub.1). (1-3)
The frequencies f where dips occur are: EQU f=(n+1/2)c/(L.sub.2 -L.sub.1). (1-4)
Plots of expressions (1-3) and (1-4) are shown in FIG. 3. In practice, B.noteq.1. Therefore, the sound pressure at dip frequencies cannot be zero and S.sub.M cannot be precisely equal to 2A/L.sub.1 at the peak frequencies. In FIG. 3, the broken line indicates the results in the case of free edge reflections merely for reference.
Further, it is assumed that the transfer function of the path of a direct wave 1-7 is represented by G.sub.1 (s) and the transfer function of the path of a reflected sound wave 1-8 is represented by G(.tau.).multidot.G(k).multidot.G.sub.2 (s), where G.sub.1 (s) and G.sub.2 (s) are transfer functions which depend on the lengths of the paths, G(.tau.) indicates the phase and delay time which depend on the difference in distance, and G(k) indicates a reflection condition such as a reflection factor.
The transfer function G.sub.A (s) between the loudspeaker 1-5 and the listening point is as follows: ##EQU2## That is, due to the factor G(.tau.), which is a function of the difference in travel distance between the two sound waves, the frequency characteristic is made irregular as shown in FIG. 3.
As is apparent from the above description, the irregularities in the frequency characteristic are attributed to the difference between the travel distance of the two sound waves. Accordingly, if the installation condition of the acoustic system or the listening position is changed, the peak and dip frequencies will also be changed. In order to compensate for this, it is possible to use a multi-band graphic equalizer 1-3, but it is considerably difficult to adjust such a device. In an acoustic system having a bass and treble controls only, it is impossible to compensate for the peaks and dips in the frequency characteristic.
FIG. 4 shows an example of a sound field. More specifically, FIG. 5 is a diagram showing the propagations of sounds in the sound field which is defined by two confronted walls. In FIG. 5, reference numeral 7-9 designates a listener. A direct sound wave 7-7L radiated from a left loudspeaker 7-5L and a sound wave 7-8R which is radiated from a right loudspeaker 7-5R and reflected by the left wall arrive the left ear of the listener 7-9. Similarly, a direct sound wave 7-7R radiated from the right loudspeaker 7-5R and a sound wave 7-8L which is radiated from the left loudspeaker 7-5L and reflected by the right wall reach the right ear of the listener 7-9.
For simplification in description, a direct wave and the first reflected wave are considered, and the correlation between the right and left ears with respect to a sound wave which is applied to the listener 7-9 in a direction will be disregarded. When signals S.sub.R and S.sub.L are applied to the right and left loudspeakers 7-5R and 7-5L, respectively, according to the above-described condition, signal sound waves represented by the following expressions (7-1) and (7-2) are applied to the right and left ears of the listener 7-9, respectively: EQU (S.sub.L /L.sub.1)e.sup.j.omega.(-L.sbsp.1.sup./c)+(S.sub.R /L.sub.4)K.sub.1 e.sup.j.omega.(-L.sbsp.4.sup./c) (7-1) EQU (S.sub.R /L.sub.3)e.sup.j.omega.(-L.sbsp.3.sup./c)+(S.sub.L /L.sub.2)K.sub.2 e.sup.j.omega.(-L.sbsp.2.sup./c) (7-2)
where c is the sound velocity, K.sub.1 and K.sub.2 are the reflection factors of the right and left walls, respectively, and L.sub.1 through L.sub.4 are the travel distances of the sound waves 7-7L, 7-8L, 7-7R and 7-8R, respectively.
In expressions (7-1) and (7-2), the second terms represent the reflected sound components to the left and right ears, respectively. In general, for stereo signal reproduction, the channel signals include only musical information necessary for satisfactory reproduction. Therefore, if, when the channel signals are radiated in the form of sound waves from the loudspeakers in the room, in addition to the direct sound waves from the loudspeakers, namely, the original signals, there are a number of reflected sound components owing to the acoustic conditions of the room, the sound signals reaching to the ears of the listener could cause excess reverberation and poor channel separation, and make the frequency characteristic irregular. That is, in this case, excellent stereo signal reproduction cannot be expected.